The orientation of the molecular chains in polymers is known to enhance some properties of the material, such as mechanical, optical, barrier, etc. In many polymer processing operations, it is desirable to induce orientation in the material, except some specific cases where any anisotropy in the material should be avoided, such as laser discs for example. This orientation in polymers can be induced by several processes such as film blowing, film tentering, blow molding, thermoforming, compression, rolling and drawing. In order to evaluate and optimize the polymer's properties and process conditions it is of tremendous importance to know the orientational states developed in the polymer.
Several techniques can be used for off-line measurement of orientation in polymers. These techniques include birefringence, infrared and other spectroscopy (FTIR, Raman, fluorescence, NMR, and others), X-ray scattering and ultrasonic techniques. Among these, birefringence, that is the anisotropy in refractive indices of the material, is the simplest. The orientation within the material can be described by the refractive index ellipsoid (indicatrix), which is defined by the refractive indices n.sub.M, n.sub.T and n.sub.N in the three axial directions known as machine, transverse and normal, which originate from the different polarizabilities in these three directions as a result of molecular chain alignment. The refractive index which is parallel to the machine direction is designated n.sub.M, the one at 90.degree. which is the transverse direction in the material plane is designated as n.sub.T, and the one in the thickness direction is n.sub.N.
Birefringence is defined as the difference between the different refractive EQU .DELTA.n.sub.MT =n.sub.M -n.sub.T EQU .DELTA.n.sub.MN =n.sub.M -n.sub.N
indices: EQU .DELTA.n.sub.TN =n.sub.T -n.sub.N
Since there are three birefringences in any material, representing the anisotropy of optical properties in three axes, the term multiaxial birefringence is used. However, in view of the fact the three birefringences are interdependent as EQU .DELTA.n.sub.TN =n.sub.T -n.sub.N =(n.sub.M -n.sub.N)-(n.sub.M -n.sub.T)=.DELTA.n.sub.MN -.DELTA.n.sub.MT
expressed by the equation:
and that it is a simple calculation to determine the third birefringence once the first two are determined, the term biaxial birefringence is commonly used in the art as necessary to define the optical properties of a sample.
On the other hand, when birefringence is only measured in one plane, the term uniaxial birefringence is used.
Birefringence can be determined in two ways, such as by the measurement of refractive indices and the calculation of their differences, or by the direct measurement of the optical retardation using polarimetry techniques. Measurement of refractive indices can be performed using a refractometer such as an Abbe refractometer for example. However, such a technique has several limitations, for instance samples with shapes may be awkward to fit the refractometer, there is generally a requirement for contact solvent and the technique is cumbersome and tedious. In addition, the use of a refractometer is not applicable for on-line monitoring.
On the other hand, polarimetry techniques generally use a monochromatic light source in an optical set-up that includes a polarizer and analyzer, between which the sample to be measured is placed to measure optical retardation.
U.S. Pat. No. 4,973,163 (Sakai et al.) discloses a method for measuring birefringence using a combination of a polarizer and analyzer, with a sample interposed between them. The combination is rotated relative to the sample to determine the relationship between the angle of rotation and the intensity of light transmitted through the arrangement. Using light at two wavelengths close to each other, the retardation can be determined. When at least three wavelengths are used, different retardation values are obtained for the respective wavelength. From the retardation values, the birefringence of the simple is calculated, but only .DELTA.n.sub.NT in the plane of the sample. This technique does fit allow the determination of multiaxial birefringence and produces uncertain results in highly oriented materials.
U.S. Pat. No. 5,406,371 (Sakai et al.) discloses a method for obtaining data to calculate retardation values using in combination a white light source with a polarizer and analyzer, that rotate in unison and between which the sample is placed. The system however does not provide the multiaxial birefringence of the sample.
U.S. Pat. No. 5,319,194 (Yoshizumi et al.) discloses a method for measuring birefringence employing a laser that emits two beams at different frequencies. After the beams have passed through the sample, the beams are split by frequency and directed to two analyzers that are polarization sensitive. The devise does not make multiaxial birefringence measurements.
U.S. Pat. No. 5,257,092 (Noguchi et al.) discloses a method for measuring birefringence with a wide polarized light beam that passes through the sample, then through a rotating polarizer, and falls on a video camera detector. The system however does not provide the multiaxial birefringence of the sample.
According to U.S. Pat. No. 4,909,630 (Gawrisch et al.), an interference image of a biaxially stretched film strip is generated optically. Streaks in the film strip are areas of different orientation and/or thickness which are distinguished from the streak-free areas in the interference image by different intensities. In order to generate the interference image, a light source, a diffuser screen and a polarizer are arranged on one side of the film strip and an analyzer and a filter are arranged on the other side of the film strip. A detector, such as a video camera, is connected to an image analysis and computing unit for evaluation of the interference image. This non-quantitative technique only determines the change in orientation and/or thickness, but not the values of biaxial birefringence.
U.S. Pat. No. 4,309,110 (Tumerman) discloses an apparatus and method for determining optical properties of a substance by passing a beam of linearly polarized light through the substance. The polarization vector of light is mechanically caused to rotate at a definite frequency, and the light is measured by a photodetector. The relative phase shift and/or modulation coefficient of this beam after passing through the substance is compared with a reference beam that has not passed through the substance, to effect measurement of linear and circular birefringence. This technique uses a single wavelength, and cannot measure biaxial birefringence. If applied to moderately and highly oriented films, it would be uncertain by a factor of 2.pi.. It has the mechanical disadvantage, compared to the present invention, of requiring rotating polarizers.
U.S. Pat. No. 4,521,111 (Paulson et al.) describes an apparatus for measuring the degree and direction of molecular orientation in a film as it advances from a stretching zone. The apparatus projects ultraviolet light which does not pass through the film but stimulates fluorescence that is detected by a part of the apparatus. This technique does not measure birefringence, but a parameter called D.sub.ex, representing the extent of orientation.
In the Japanese application JP93163005, a method and instrument for measuring retardation is disclosed. Its purpose is however to measure the retardation of a high polymer film or sheet having small anisotropy on line in the manufacturing process of the film or sheet by imposing a phase plate having known retardation between a polarizing section and analyzing section and the sheet to be measured between the phase plate and the analyzing section. This technique does not apply to high anisotropies and biaxial birefringences.
Canadian Patent 1,153,578 (Pindera) teaches a method for the optical measurement in mechanics using scattered light techniques. Specifically, this method relates to opto-mechanical apparatus which is useful for the rapid, accurate and theoretically correct measurements of the stress-induced birefringence, and, in particular, to determine cross-sections through elastic isodynes which carry information on the normal and shear stress components. The measurements are mentioned to be simpler when the patterns of light scattering are close to the Rayleigh model of scattering. However, this procedure is not applicable to the determination of the absolute biaxial birefringence of moderately and highly oriented materials.
In the non-patent literature, some studies mention techniques for the measurement of birefringence of materials, as described below with their advantages and disadvantages.
Abetz and Fuller, Rheol. Acta, 29, 11 (1990), describe a method that solves the problem of determining the correct birefringence and orientation angle of samples having multiple orders of retardation. The approach simultaneously uses two wavelengths of light combined with modulation of the polarization vector using a high speed rotating half wave plate, which is an achromatic wave plate. The technique is demonstrated for multiple orders in retardation. However, this method does not apply to biaxially oriented materials.
R. D. L. Marsh, J. C. Duncan and S. Brister, J. Thermal Analysis, 45, 891 (1995) published a paper on the measurement of dynamic optical birefringence, in which complex birefringence, strain and stress-optical coefficients are determined simultaneously with complex mechanical properties. Both used monochromatic light with the disadvantages mentioned above.
Hongladarom and Burghardt, Macromolecules, 26, 785 (1993), and Beekmans and de Boer, Macromolecules, 29, 8726 (1996), used a spectrographic technique for the determination of orientation of liquid crystalline polymers solutions due to their high anisotropy. This technique uses a multiwavelength source but was limited to normal incidence. The calculation procedure was not rigorous, because in the first paper (1993), the wavelength dependence of birefringence was arbitrary, and in the second paper (1996) it was not taken properly into account but approximated over a short wavelength interval. The procedure does not allow determination of biaxial birefringence.
Takahashi and Fuller (Rheol. Acta, 35, 97 (1996)) and Hongladarom and Burghardt (Macromolecules, 27, 483 (1994)) described a procedure to measure the full refractive index of solutions with a monochromatic light source and an oblique incidence. The procedure and technique described does not allow measurement of absolute birefringence of highly oriented materials.
From these examples of the prior art, it is evident that, according to present knowledge, uniaxial birefringence measurement can be accomplished in a number of ways. However, the prior art does not disclose methods or apparatus capable of making on-line biaxial birefringence measurements in samples such as moderately or highly oriented, monolayer or multilayer films, sheets or shapes in order to determine the biaxial and thus multiaxial birefingence of the samples in absolute, mathematically certain terms.